On totally decomposable algebras with involution in characteristic two

2015/03/15 by M. G. Mahmoudi, Mahmoudi, M. G., A.‐H. Nokhodkar +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1503.04418

openalex publication_date 2015/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogonal type.

Citations

• Finite-Dimensional Division Algebras over Fields
• Square-Central and Artin-Schreier Elements in Division Algebras

Related

• Decomposability of orthogonal involutions in degree 12
• Involutions on tensor products of quaternion algebras
• Symmetric square-central elements in products of orthogonal involutions in characteristic two
• Orthogonal involutions and totally singular quadratic forms in characteristic two
• On split products of quaternion algebras with involution in characteristic two